Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions

TL;DR

This paper calculates critical exponents and scaling functions for disordered elastic interfaces at 3-loop order, advancing theoretical understanding of their equilibrium properties in various dimensions.

Contribution

It provides the first 3-loop order calculations of critical exponents and the full 2-point function for disordered elastic manifolds in equilibrium.

Findings

Critical exponents for roughness and correction-to-scaling up to 3-loop order.

Full 2-point function computed up to 2-loop order.

Enhanced theoretical precision in the field theory of disordered elastic interfaces.

Abstract

For disordered elastic manifolds in the ground state (equilibrium) we obtain the critical exponents for the roughness and the correction-to-scaling up to 3-loop order, i.e. third order in $\epsilon=4-d$, where $d$ is the internal dimension $d$. We also give the full 2-point function up to order $\epsilon^{2}$, i.e. at 2-loop order.